Fluctuating Interfaces in Liquid Crystals

TL;DR

This paper reviews recent theoretical and simulation studies on the fluctuating interfaces between nematic and isotropic liquid-crystalline phases, highlighting anisotropic interfacial tension and comparing predictions with simulation results.

Contribution

It combines analytical Landau-de Gennes theory with molecular simulations to analyze capillary wave spectra and interfacial tension anisotropy in liquid crystals.

Findings

Good agreement between theory and simulation in the stiff director regime.

Interfacial tension is anisotropic at small wavelengths and isotropic at large wavelengths.

Crossover to flexible director regime occurs at wavelengths beyond current simulation capabilities.

Abstract

We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.